Thanks to their fast start, the Yankees have turned themselves into legitimate playoff contenders. The math says it. And when the numbers add up, anyone can feel confident that his team will be playing at least one game after the scheduled 162.

They need only play two games above .500 — 66-64 — in the 130 games remaining to reach the 87-win mark.

There’s no saying that 87 wins gets them in, of course. Toronto and Baltimore both needed 89 wins to get into last year’s wild card game. But on the brighter side, the Astros needed only 86 to face the Yanks, and beat them, the year before.

The point is, even if one accounts for some upward wiggle room, the Yanks have placed themselves in as good as any position short of a can’t-miss in their first 32 games.

Nobody thought that was possible to begin with. The Yanks are already well ahead of the game in that respect. And in truth, Joe Girardi’s group of youngsters isn’t going to continue winning at its current .677 rate. Young position players plus mediocre starting pitching dictate that the surprising, blinding success rate must come down.

That could well happen this weekend against the Astros, baseball’s best team at 24-11. But no matter what happens during the remainder of this series, the Yankee have proved enough for hope-filled disciples to believe they’ll never fall that far from contention.

It is one thing, after all, to descend from near .700 ball to .500. It’s quite another, even for a young team, to crash and burn their way to 10-under.

Though they sit atop the division, the Yankees are probably not good enough yet to win it outright, as mouth-watering as that concept sounds right now. But the pitching, regarded as no less than suspect when training camp broke, appears just strong enough to keep them in a wild card race.

Out of Masahiro Tanaka, CC Sabathia, Michael Pineda, Luis Severino, and Jordan Montgomery, only Sabathia looks like a major problem. He had his fourth straight poor outing Tuesday, allowing five runs and seven hits over six innings against the Reds. At 5.77, his ERA stands as the worst among the starters.

For now, Girardi can afford to put up with Sabathia’s problems. The others are doing better than expected. Severino, for instance, couldn’t find his way into the fifth inning last year. But now he’s 2-2 with a 3.40 ERA, while holding opponents to a .200 batting average.

Even Pineda has found some consistency, as he is 3-2 with a 3.27 ERA after going 6 2/3 strong innings during Thursday’s 3-2 loss to the Astros. And Tanaka is, as expected, the ace at 5-1, though his 4.36 ERA is somewhat surprising.

All of the starting arms, of course, have benefited from a bullpen that has turned Yankee games into seven-inning affairs. The relief corps stood third in the majors with a 2.55 ERA and a .199 opponents BA before Adam Warren, Jonathan Holder, and Chasen Shreve held Houston scoreless over the final 2 1/3 innings in the opener.

As long as the other starters continue to stay on a solid course, Sabathia’s spot in the rotation will be secure. But ultimately, the Yanks may have to work a late July trade if the old warhorse doesn’t come around.

The young hitters have spoken for themselves. Aaron Judge (.308), Aaron Hicks (.333), Gary Sanchez (.262), and Ronald Torreyes (.305) will probably cool off somewhat, but all indications point to them remaining effective barring injury. And now that Brett Gardner (.259) has come around to join Starlin Castro (.351), Chase Headley (.267), and Jacoby Ellsbury (.280) to solidify an already dangerous lineup, an injury epidemic is the only real fear the Yanks should have.

Barring that, they have placed themselves in excellent position for a playoff spot. A division championship may still be a year or two away.

But if 87 to 89 wins is going to earn a wild card spot this year, then feel free to believe the Yankees will get one of those two slots.